Delta-sigma modulators are commonly used for converting between analog signals and digital signals and converting from a high sample rate to a low sample rate, and may be implemented for example, in a digital-to-analog converter, analog-to-digital converter, or a delta-sigma phase locked loop (PLL). An error feedback delta sigma modulator may be used in certain designs for added stability. An example of a second order error feedback delta-sigma modulator 100 is illustrated in FIG. 1. In the illustrated example, an input signal u is combined with an output of a feedback filter 110 to generate a modified input signal y having a first sample rate n. The modified input signal y is provided to a quantizer 104, which outputs a corresponding signal v at a lower sample rate m. The quantizer 104 introduces quantization error E when the least significant bits of the modified input signal y are removed to form the output signal v. The quantized value v is fed into the feedback filter 110 to generate a correction to be applied in the next iteration. The quantized value v is subtracted from the input signal y at 108 to produce the error value E. The error E is fed back to the input signal through the feedback filter 110, having an impulse response given by the transfer function Hf(z)=−2z−1+z−2. The z-domain output of the feedback filter 110 is combined with the input signal at 112 to produce the modified input signal y. Using the delta-sigma demodulator 100, the output signal v can represent the input signal u, but with less bits, in average fashion.
One drawback with conventional delta-sigma modulators, such as delta-sigma modulator 100, is that when the input signal is zero (or very small), the output signal may continue to produce a series of output values. For example, when the signal is zero or very small or a dc signal that includes only most significant bits (MSBs), but without least-significant bits (LSBs), a delta-sigma output can form a limited cycle outputting signals between 0 and 1, which can degrade out-of-band noise. Out-of-band noise may get aliased back into the baseband signal due to limited bandwidth of an analog digital to analog converter following this digital delta sigma modulator. System requirements for some applications, such as audio headphones applications, may require out of band noise to be below certain level for final line-out or headphone output. Thus, there is a continued need to improve the performance of delta-sigma modulators.